Chapter 15
Capital Structure Decisions
ANSWERS TO END-OF-CHAPTER QUESTIONS
15-1 a. Capital structure is the manner in which a firm’s assets are financed; that is, the
right-hand side of the balance sheet. Capital structure is normally expressed as the
percentage of each type of capital used by the firm–debt, preferred stock, and
common equity. Business risk is the risk inherent in the operations of the firm, prior
b. Operating leverage is the extent to which fixed costs are used in a firm’s operations.
If a high percentage of a firm’s total costs are fixed costs, then the firm is said to have
a high degree of operating leverage. Operating leverage is a measure of one element
of business risk, but does not include the second major element, sales variability.
c. Reserve borrowing capacity exists when a firm uses less debt under “normal”
15-4 Operating leverage affects EBIT and, through EBIT, EPS. Financial leverage has no
effect on EBIT–it only affects EPS, given EBIT.
15-5 If sales tend to fluctuate widely, then cash flows and the ability to service fixed charges
will also vary. Such a firm is said to have high business risk. Consequently, there is a
15-6 Public utilities place greater emphasis on long-term debt because they have more stable
sales and profits as well as more fixed assets. Also, utilities have fixed assets which can
15-7 EBIT depends on sales and operating costs. Interest is deducted from EBIT. At high debt
levels, firms lose business, employees worry, and operations are not continuous because
15-8 The tax benefits from debt increase linearly, which causes a continuous increase in the
15-9 If equity is viewed as an option on the total value of the firm with a strike price equal to
the face value of debt then the equity value should be affected by risk in the same way
that an option is affected by risk. An option is worth more if the underlying asset is more
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
15-2 If wd = 0.2, then wce = 1 – 0.2 = 0.8. So D/S = wd/we = 0.2/0.8.
15-3 If the company had no debt, its required return would be:
15-6 nPost = Original shares – shares repurchased
= nPrior – (Dollar value of shares repurchased/Repurchase Price)
Note that the formula
nPost = nPrior [(VOpNew – DNew)/(VOpNew – DOld)] can be used if you note that
15-7 a. Here are the steps involved:
(1) Determine the variable cost per unit at present, V:
Profit = P(Q) – FC – V(Q)
(2) Determine the new profit level if the change is made:
New profit = P2(Q2) – FC2 – V2(Q2)
(3) Determine the incremental profit:
(4) Estimate the approximate rate of return on new investment:
Since the return exceeds the 15 percent cost of equity, this analysis suggests that the
firm should go ahead with the change.
b. The change would increase the breakeven point:
Old:
)Q(VFC
FC
=
000,500,2$000,000,2$
000,000,2$
= 44.44%.
New:
)Q(VFC
FC
222
2
=
000,800,2$000,500,2$
000,500,2$
= 47.17%.
The change in breakeven points–and also the higher percentage of fixed
costs–suggests that the new situation is more risky.
15-8 a. Original value of the firm (D = $0):
We are given that the book value of assets is equal to the market value of assets, so
Original cost of capital:
WACC = wd rd(1-T) + wcers
With financial leverage (wd=30%):
WACC = wd rd(1-T) + wcers
Because growth is zero, FCF is equal to EBIT(1-T). The value of operations is:
Vop =
.286.214,348,3$
0896.0
)40.01)(000,500($
WACC
)T1)(EBIT(
WACC
FCF
Increasing the financial leverage by adding $900,000 of debt results in an increase in
the firm’s value from $3,000,000 to $3,348,214.286.
b. Using its target capital structure of 30% debt, the company must have debt of:
Therefore, its value of equity is:
The new price per share, P, is:
c. The number of shares repurchased, X, is:
The number of remaining shares, n, is:
Initial position:
EPS = NI/n0
= [(EBIT – Int.)(1-T)] / n0
With financial leverage:
EPS = [($500,000 – 0.07($1,004,464.286))(1-0.40)] / 140,000
d. 30% debt: TIE =
I
EBIT
=
5.312,70$
EBIT
.
Probability TIE
0.10 ( 1.42)
0.20 2.84
The interest payment is not covered when TIE < 1.0. The probability of this
occurring is 0.10, or 10 percent.
15-9 a. Present situation (50% debt):
WACC = wd rd(1-T) + wcers
1125.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF
70 percent debt:
WACC = wd rd(1-T) + wcers
1194.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF
30 percent debt:
WACC = wd rd(1-T) + wcers
1114.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF
b. b = bU (1 + (1-T)(D/S)).
c. WACC = wd rd(1-T) + wcers
08683.0
)4.01)(933.14($
WACC
)T1)(EBIT(
WACC
FCF
15-11 Tax rate = 40% rRF = 5.0%
From data given in the problem and table we can develop the following table:
wdwce D/S rdrd(1 – T)
Levered
betaarsbWACCc
0 100% 0.00 6.0% 3.60% 0.80 9.80% 9.80%
0.2 80% 0.25 7.0% 4.20% 0.92 10.52% 9.26%
Notes:
a These beta estimates were calculated using the Hamada equation,
b = bU[1 + (1 – T)(D/S)].
b These rs estimates were calculated using the CAPM, rs = rRF + (rM – rRF)b.
c These WACC estimates were calculated with the following equation:
WACC = wd(rd)(1 – T) + (wce)(rs).
The firm’s optimal capital structure is that capital structure which minimizes the firm’s
WACC. The WACC is minimized at a capital structure consisting of 60% debt and 40%
equity. At that capital structure, the firm’s WACC is 8.89%.
15-12 a. The inputs to the Black and Scholes option pricing model are P = 5, X = 2, rRF = 6%,
= 50%, and t = 2 years. Given these inputs, the value of a call option is calculated
as:
t
t]2/r[)X/Pln(
d
2
RF
1
=
8191.1
25.0
2]2/5.006.0[)2/5ln( 2
.
tdd
12
=
1120.125.0819.1
.
Using Excel’s NORMSDIST function N(d1) = 0.9656, and N(d2) = 0.8669.
This gives a value of the call option equal to:
)][N(dXe)]P[N(dV
2
t-r
1
RF
=
3.29 [0.8669]2e5[0.9656]
)2(06.0-
million